Physics-informed machine learning emerges as a transformative approach, bridging the gap between the high fidelity of mechanistic models and the adaptive, data-driven insights afforded by artificial intelligence and machine learning. In the realm of chemical reaction network modeling, this synergy is particularly valuable. It offers a solution to the prohibitive computational costs associated with detailed mechanistic models, while also capitalizing on the predictive power and flexibility of machine learning algorithms. This study exemplifies this innovative fusion by applying it to the critical biomedical challenge of A$\beta$ fibril aggregation, shedding light on the mechanisms underlying Alzheimer's disease. A cornerstone of this research is the introduction of an automatic reaction order model reduction framework, tailored to optimize the scale of reduced order kinetic models. This framework is not merely a technical enhancement; it represents a paradigm shift in how models are constructed and refined. By automatically determining the most appropriate level of detail for modeling reaction networks, our proposed approach significantly enhances the efficiency and accuracy of simulations. This is particularly crucial for systems like A$\beta$ aggregation, where the precise characterization of nucleation and growth kinetics can provide insights into potential therapeutic targets. The potential generalizability of this automatic model reduction technique to other network models is a key highlight of this study. The methodology developed here has far-reaching implications, offering a scalable and adaptable tool for a wide range of applications beyond biomedical research. The ability to dynamically adjust model complexity in response to the specific demands of the system under study is a powerful asset. This flexibility ensures that the models remain both computationally feasible and scientifically relevant, capable of accommodating new data and evolving understandings of complex phenomena.

The training data for each of the eight amyloid-B binning models is found inside the "binning_trials" folder, inside of which are the results and statistics for each of the PINN models located in their respective folders inside the "models" folder. Eight Jupyter notebooks contain scripts that create and train PINNs for each binning structure. the "abeta.ipynb" notebook serves as the blueprint code, using the 6-species model to train a PINN. The PINN building and training tools are used from the DeepXDE python library, a modified version of which can be found in the "deepxdeAbeta" folder.